Finite Group DatabasebetaFinite Group Databasebeta| order | 31020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic7755 |
| unambiguous semidirect product | C3⋊Dic2585 |
| unambiguous semidirect product | C11⋊Dic705 |
| unambiguous semidirect product | C47⋊Dic165 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7755 |
| commutator, hypocenter | C3×C5×C11×C47 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C11×C47 | C2 |
| LCS | G ▷ C3×C5×C11×C47 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 31020 |
A minimal faithful permutation representation — 2 generators on 70 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70);(1,3,2,4)(6,7)(9,12)(10,11)(14,23)(15,22)(16,21)(17,20)(18,19)(25,70)(26,69)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)Polycyclic presentation:
2,3,5,11,47,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^467758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic15510 |
| maximal normal subgroup of | Dic15510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31020, 17);